Seminar | October 28 | 3:10-5 p.m. | 740 Evans Hall
Peter Whang, MIT
Moduli spaces for special linear rank two local systems (with prescribed boundary traces) on topological surfaces are basic objects in geometry. After motivating their Diophantine study, we use mapping class group dynamics and differential geometric tools to establish a structure theorem for the integral points of these varieties, showing that they are finitely generated in a suitable sense and generalizing work of Markoff (1880). This invites an analogy with classical finite generation results on algebraic tori and abelian varieties, and motivates the Diophantine analysis of subvarieties on the moduli spaces. In this direction, we give an effective analysis of integral points for nondegenerate algebraic curves.